Elementary Algebra
Introduction to Algebra Linear Equations and Inequalities Functions and Graphs I Lines and thier Graphs Linear Systems Exponents & Polynomials
Intermediate Algebra
Factoring Rational Expressions Rational Equations and Applications Radical Expressions Nonlinear Equations and Applications Functions and Graphs II Exponential and Logarithmic Functions
Precalculus I / College Algebra
Equations and Inequalitites Functions and Graphs Polynomial and Rational Functions Exponential and Logarithmic Functions Systems and Matrices Geometry Basics Conic Sections Sequences and Series
Precalculus II / Trigonometry
The Six Trigonometric Functions Right Triangle Trigonometry Circular Functions Graphs of Trigonometric Functions Trigonometric Identities Trigonometric Equations Oblique Triangles and the Laws Vectors Complex, Parametric, and Polar Forms
Calculus I
Limits and Continuity Derivatives Analysis of Curves Antiderivatives
Calculus II
Transcendental Functions
Geometry Physics Integration Techniques Calculus of Infinity Parametric, Polar, and Conic Curves
Calculus III

Course: College Algebra
Topic: Polynomial and Rational Functions
Subtopic: Polynomial Functions II - Division, Remainder Thm, Factor Thm

Overview

Continuing our study of polynomial functions, in this lesson we concentrate on two important theorems that will enable us to find roots of the functions which in term will enable us to factor the polynomial completely. The ultimate goal is to turn a long polynomial in general form into a product of linear factors.

Objectives

By the end of this topic you should know and be prepared to be tested on:

• 3.3.1 Perform synthetic division
• 3.3.2 Use synthetic division to simplify rational expressions whose denominator is a linear expression of the form (x +- c)
• 3.3.3 Understand and be able to apply the remainder theorem and the factor theorem
• 3.3.4 Use synthetic division to determine if a given number is a zero of the polynomial
• 3.3.5 Know the connection between zeros, roots, and x-intercept points
• 3.3.6 Use theorems and synthetic division to factor a polnomial in the rational realm, real realm, or complex realm
• 3.3.7 Find a polynomial that has given roots

Terminology

Terms you should be able to define: synthetic division, zero, root, remainder theorem, factor theorem, rational vs. real vs. complex realm

Mini-Lectures and Examples

Supplemental Resources (optional)

If you need supplemental tutorial videos with examples relevant to this section go to James Sousa's MathIsPower4U and search for topics:
"Determining the Characteristics of Polynomial Functions"
"Finding the Zeros of Polynomial Functions"

rev. 2020-10-10